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<!-- ==================== MODULE DESCRIPTION ==================== -->
<h1 class="epydoc">Module Integration</h1><p class="nomargin-top"><span class="codelink"><a href="dadi.Integration-pysrc.html">source&nbsp;code</a></span></p>
<pre class="literalblock">

Functions for integrating population frequency spectra.

</pre>

<!-- ==================== FUNCTIONS ==================== -->
<a name="section-Functions"></a>
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<tr>
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      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
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        <tr>
          <td><span class="summary-sig"><a href="dadi.Integration-module.html#set_timescale_factor" class="summary-sig-name">set_timescale_factor</a>(<span class="summary-sig-arg">pts</span>,
        <span class="summary-sig-arg">factor</span>=<span class="summary-sig-default">10</span>)</span><br />
      Controls the fineness of timesteps during integration.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#set_timescale_factor">source&nbsp;code</a></span>
            
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    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_inject_mutations_1D"></a><span class="summary-sig-name">_inject_mutations_1D</span>(<span class="summary-sig-arg">phi</span>,
        <span class="summary-sig-arg">dt</span>,
        <span class="summary-sig-arg">xx</span>,
        <span class="summary-sig-arg">theta0</span>)</span><br />
      Inject novel mutations for a timestep.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_inject_mutations_1D">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_inject_mutations_2D"></a><span class="summary-sig-name">_inject_mutations_2D</span>(<span class="summary-sig-arg">phi</span>,
        <span class="summary-sig-arg">dt</span>,
        <span class="summary-sig-arg">xx</span>,
        <span class="summary-sig-arg">yy</span>,
        <span class="summary-sig-arg">theta0</span>,
        <span class="summary-sig-arg">frozen1</span>,
        <span class="summary-sig-arg">frozen2</span>)</span><br />
      Inject novel mutations for a timestep.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_inject_mutations_2D">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_inject_mutations_3D"></a><span class="summary-sig-name">_inject_mutations_3D</span>(<span class="summary-sig-arg">phi</span>,
        <span class="summary-sig-arg">dt</span>,
        <span class="summary-sig-arg">xx</span>,
        <span class="summary-sig-arg">yy</span>,
        <span class="summary-sig-arg">zz</span>,
        <span class="summary-sig-arg">theta0</span>,
        <span class="summary-sig-arg">frozen1</span>,
        <span class="summary-sig-arg">frozen2</span>,
        <span class="summary-sig-arg">frozen3</span>)</span><br />
      Inject novel mutations for a timestep.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_inject_mutations_3D">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a href="dadi.Integration-module.html#_compute_dt" class="summary-sig-name" onclick="show_private();">_compute_dt</a>(<span class="summary-sig-arg">dx</span>,
        <span class="summary-sig-arg">nu</span>,
        <span class="summary-sig-arg">ms</span>,
        <span class="summary-sig-arg">gamma</span>,
        <span class="summary-sig-arg">h</span>)</span><br />
      Compute the appropriate timestep given the current demographic params.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_compute_dt">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr>
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a href="dadi.Integration-module.html#one_pop" class="summary-sig-name">one_pop</a>(<span class="summary-sig-arg">phi</span>,
        <span class="summary-sig-arg">xx</span>,
        <span class="summary-sig-arg">T</span>,
        <span class="summary-sig-arg">nu</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">gamma</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">h</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">theta0</span>=<span class="summary-sig-default">1.0</span>,
        <span class="summary-sig-arg">initial_t</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">frozen</span>=<span class="summary-sig-default">False</span>,
        <span class="summary-sig-arg">beta</span>=<span class="summary-sig-default">1</span>)</span><br />
      Integrate a 1-dimensional phi foward.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#one_pop">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr>
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a href="dadi.Integration-module.html#two_pops" class="summary-sig-name">two_pops</a>(<span class="summary-sig-arg">phi</span>,
        <span class="summary-sig-arg">xx</span>,
        <span class="summary-sig-arg">T</span>,
        <span class="summary-sig-arg">nu1</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">nu2</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">m12</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">m21</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">gamma1</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">gamma2</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">h1</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">h2</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">theta0</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">initial_t</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">frozen1</span>=<span class="summary-sig-default">False</span>,
        <span class="summary-sig-arg">frozen2</span>=<span class="summary-sig-default">False</span>)</span><br />
      Integrate a 2-dimensional phi foward.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#two_pops">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr>
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a href="dadi.Integration-module.html#three_pops" class="summary-sig-name">three_pops</a>(<span class="summary-sig-arg">phi</span>,
        <span class="summary-sig-arg">xx</span>,
        <span class="summary-sig-arg">T</span>,
        <span class="summary-sig-arg">nu1</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">nu2</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">nu3</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">m12</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">m13</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">m21</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">m23</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">m31</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">m32</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">gamma1</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">gamma2</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">gamma3</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">h1</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">h2</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">h3</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">theta0</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">initial_t</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">frozen1</span>=<span class="summary-sig-default">False</span>,
        <span class="summary-sig-arg">frozen2</span>=<span class="summary-sig-default">False</span>,
        <span class="summary-sig-arg">frozen3</span>=<span class="summary-sig-default">False</span>)</span><br />
      Integrate a 3-dimensional phi foward.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#three_pops">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_Vfunc"></a><span class="summary-sig-name">_Vfunc</span>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">nu</span>,
        <span class="summary-sig-arg">beta</span>=<span class="summary-sig-default">1</span>)</span></td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_Vfunc">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_Mfunc1D"></a><span class="summary-sig-name">_Mfunc1D</span>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">gamma</span>,
        <span class="summary-sig-arg">h</span>)</span></td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_Mfunc1D">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_Mfunc2D"></a><span class="summary-sig-name">_Mfunc2D</span>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>,
        <span class="summary-sig-arg">mxy</span>,
        <span class="summary-sig-arg">gamma</span>,
        <span class="summary-sig-arg">h</span>)</span></td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_Mfunc2D">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_Mfunc3D"></a><span class="summary-sig-name">_Mfunc3D</span>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>,
        <span class="summary-sig-arg">z</span>,
        <span class="summary-sig-arg">mxy</span>,
        <span class="summary-sig-arg">mxz</span>,
        <span class="summary-sig-arg">gamma</span>,
        <span class="summary-sig-arg">h</span>)</span></td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_Mfunc3D">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_compute_dfactor"></a><span class="summary-sig-name">_compute_dfactor</span>(<span class="summary-sig-arg">dx</span>)</span><br />
      \Delta_j from the paper.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_compute_dfactor">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a href="dadi.Integration-module.html#_compute_delj" class="summary-sig-name" onclick="show_private();">_compute_delj</a>(<span class="summary-sig-arg">dx</span>,
        <span class="summary-sig-arg">MInt</span>,
        <span class="summary-sig-arg">VInt</span>,
        <span class="summary-sig-arg">axis</span>=<span class="summary-sig-default">0</span>)</span><br />
      Chang an Cooper's \delta_j term.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_compute_delj">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a href="dadi.Integration-module.html#_one_pop_const_params" class="summary-sig-name" onclick="show_private();">_one_pop_const_params</a>(<span class="summary-sig-arg">phi</span>,
        <span class="summary-sig-arg">xx</span>,
        <span class="summary-sig-arg">T</span>,
        <span class="summary-sig-arg">nu</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">gamma</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">h</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">theta0</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">initial_t</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">beta</span>=<span class="summary-sig-default">1</span>)</span><br />
      Integrate one population with constant parameters.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_one_pop_const_params">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_two_pops_const_params"></a><span class="summary-sig-name">_two_pops_const_params</span>(<span class="summary-sig-arg">phi</span>,
        <span class="summary-sig-arg">xx</span>,
        <span class="summary-sig-arg">T</span>,
        <span class="summary-sig-arg">nu1</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">nu2</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">m12</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">m21</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">gamma1</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">gamma2</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">h1</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">h2</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">theta0</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">initial_t</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">frozen1</span>=<span class="summary-sig-default">False</span>,
        <span class="summary-sig-arg">frozen2</span>=<span class="summary-sig-default">False</span>)</span><br />
      Integrate two populations with constant parameters.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_two_pops_const_params">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_three_pops_const_params"></a><span class="summary-sig-name">_three_pops_const_params</span>(<span class="summary-sig-arg">phi</span>,
        <span class="summary-sig-arg">xx</span>,
        <span class="summary-sig-arg">T</span>,
        <span class="summary-sig-arg">nu1</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">nu2</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">nu3</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">m12</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">m13</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">m21</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">m23</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">m31</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">m32</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">gamma1</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">gamma2</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">gamma3</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">h1</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">h2</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">h3</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">theta0</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">initial_t</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">frozen1</span>=<span class="summary-sig-default">False</span>,
        <span class="summary-sig-arg">frozen2</span>=<span class="summary-sig-default">False</span>,
        <span class="summary-sig-arg">frozen3</span>=<span class="summary-sig-default">False</span>)</span><br />
      Integrate three population with constant parameters.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_three_pops_const_params">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_Vfunc_X"></a><span class="summary-sig-name">_Vfunc_X</span>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">nu</span>,
        <span class="summary-sig-arg">beta</span>)</span></td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_Vfunc_X">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_Mfunc1D_X"></a><span class="summary-sig-name">_Mfunc1D_X</span>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">gamma</span>,
        <span class="summary-sig-arg">h</span>,
        <span class="summary-sig-arg">beta</span>)</span></td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_Mfunc1D_X">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a name="_inject_mutations_1D_X"></a><span class="summary-sig-name">_inject_mutations_1D_X</span>(<span class="summary-sig-arg">phi</span>,
        <span class="summary-sig-arg">dt</span>,
        <span class="summary-sig-arg">xx</span>,
        <span class="summary-sig-arg">theta0</span>,
        <span class="summary-sig-arg">beta</span>,
        <span class="summary-sig-arg">alpha</span>)</span><br />
      Inject novel mutations for a timestep.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_inject_mutations_1D_X">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr>
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a href="dadi.Integration-module.html#one_pop_X" class="summary-sig-name">one_pop_X</a>(<span class="summary-sig-arg">phi</span>,
        <span class="summary-sig-arg">xx</span>,
        <span class="summary-sig-arg">T</span>,
        <span class="summary-sig-arg">nu</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">gamma</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">h</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">beta</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">alpha</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">theta0</span>=<span class="summary-sig-default">1.0</span>,
        <span class="summary-sig-arg">initial_t</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">frozen</span>=<span class="summary-sig-default">False</span>)</span><br />
      Integrate a 1-dimensional phi foward.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#one_pop_X">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
<tr class="private">
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
      <table width="100%" cellpadding="0" cellspacing="0" border="0">
        <tr>
          <td><span class="summary-sig"><a href="dadi.Integration-module.html#_one_pop_const_params_X" class="summary-sig-name" onclick="show_private();">_one_pop_const_params_X</a>(<span class="summary-sig-arg">phi</span>,
        <span class="summary-sig-arg">xx</span>,
        <span class="summary-sig-arg">T</span>,
        <span class="summary-sig-arg">nu</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">gamma</span>=<span class="summary-sig-default">0</span>,
        <span class="summary-sig-arg">h</span>=<span class="summary-sig-default">0.5</span>,
        <span class="summary-sig-arg">beta</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">alpha</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">theta0</span>=<span class="summary-sig-default">1</span>,
        <span class="summary-sig-arg">initial_t</span>=<span class="summary-sig-default">0</span>)</span><br />
      Integrate one population with constant parameters.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="dadi.Integration-pysrc.html#_one_pop_const_params_X">source&nbsp;code</a></span>
            
          </td>
        </tr>
      </table>
      
    </td>
  </tr>
</table>
<!-- ==================== VARIABLES ==================== -->
<a name="section-Variables"></a>
<table class="summary" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr bgcolor="#70b0f0" class="table-header">
  <td colspan="2" class="table-header">
    <table border="0" cellpadding="0" cellspacing="0" width="100%">
      <tr valign="top">
        <td align="left"><span class="table-header">Variables</span></td>
        <td align="right" valign="top"
         ><span class="options">[<a href="#section-Variables"
         class="privatelink" onclick="toggle_private();"
         >hide private</a>]</span></td>
      </tr>
    </table>
  </td>
</tr>
<tr>
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
        <a name="logger"></a><span class="summary-name">logger</span> = <code title="logging.getLogger('Integration')">logging.getLogger('Integration')</code>
    </td>
  </tr>
<tr>
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
        <a name="use_delj_trick"></a><span class="summary-name">use_delj_trick</span> = <code title="False">False</code>
    </td>
  </tr>
<tr>
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
        <a name="timescale_factor"></a><span class="summary-name">timescale_factor</span> = <code title="0.001">0.001</code>
    </td>
  </tr>
<tr>
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
        <a name="use_old_timestep"></a><span class="summary-name">use_old_timestep</span> = <code title="False">False</code>
    </td>
  </tr>
<tr>
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
        <a name="old_timescale_factor"></a><span class="summary-name">old_timescale_factor</span> = <code title="0.1">0.1</code>
    </td>
  </tr>
<tr>
    <td width="15%" align="right" valign="top" class="summary">
      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
        <a name="__package__"></a><span class="summary-name">__package__</span> = <code title="'dadi'"><code class="variable-quote">'</code><code class="variable-string">dadi</code><code class="variable-quote">'</code></code>
    </td>
  </tr>
</table>
<!-- ==================== FUNCTION DETAILS ==================== -->
<a name="section-FunctionDetails"></a>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr bgcolor="#70b0f0" class="table-header">
  <td colspan="2" class="table-header">
    <table border="0" cellpadding="0" cellspacing="0" width="100%">
      <tr valign="top">
        <td align="left"><span class="table-header">Function Details</span></td>
        <td align="right" valign="top"
         ><span class="options">[<a href="#section-FunctionDetails"
         class="privatelink" onclick="toggle_private();"
         >hide private</a>]</span></td>
      </tr>
    </table>
  </td>
</tr>
</table>
<a name="set_timescale_factor"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">set_timescale_factor</span>(<span class="sig-arg">pts</span>,
        <span class="sig-arg">factor</span>=<span class="sig-default">10</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="dadi.Integration-pysrc.html#set_timescale_factor">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">

Controls the fineness of timesteps during integration.

The timestep will be proportional to Numerics.default_grid(pts)[1]/factor.
Typically, pts should be set to the *largest* number of grid points used in
extrapolation. 

An adjustment factor of 10 typically results in acceptable accuracy. It may
be desirable to increase this factor, particularly when population sizes
are changing continously and rapidly.

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="_compute_dt"></a>
<div class="private">
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_compute_dt</span>(<span class="sig-arg">dx</span>,
        <span class="sig-arg">nu</span>,
        <span class="sig-arg">ms</span>,
        <span class="sig-arg">gamma</span>,
        <span class="sig-arg">h</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="dadi.Integration-pysrc.html#_compute_dt">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">

Compute the appropriate timestep given the current demographic params.

This is based on the maximum V or M expected in this direction. The
timestep is scaled such that if the params are rescaled correctly by a
constant, the exact same integration happens. (This is equivalent to
multiplying the eqn through by some other 2N...)

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="one_pop"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">one_pop</span>(<span class="sig-arg">phi</span>,
        <span class="sig-arg">xx</span>,
        <span class="sig-arg">T</span>,
        <span class="sig-arg">nu</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">gamma</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">h</span>=<span class="sig-default">0.5</span>,
        <span class="sig-arg">theta0</span>=<span class="sig-default">1.0</span>,
        <span class="sig-arg">initial_t</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">frozen</span>=<span class="sig-default">False</span>,
        <span class="sig-arg">beta</span>=<span class="sig-default">1</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="dadi.Integration-pysrc.html#one_pop">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">

Integrate a 1-dimensional phi foward.

phi: Initial 1-dimensional phi
xx: Grid upon (0,1) overwhich phi is defined.

nu, gamma, and theta0 may be functions of time.
nu: Population size
gamma: Selection coefficient on *all* segregating alleles
h: Dominance coefficient. h = 0.5 corresponds to genic selection. 
   Heterozygotes have fitness 1+2sh and homozygotes have fitness 1+2s.
theta0: Propotional to ancestral size. Typically constant.
beta: Breeding ratio, beta=Nf/Nm.

T: Time at which to halt integration
initial_t: Time at which to start integration. (Note that this only matters
           if one of the demographic parameters is a function of time.)

frozen: If True, population is 'frozen' so that it does not change.
        In the one_pop case, this is equivalent to not running the
        integration at all.

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="two_pops"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">two_pops</span>(<span class="sig-arg">phi</span>,
        <span class="sig-arg">xx</span>,
        <span class="sig-arg">T</span>,
        <span class="sig-arg">nu1</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">nu2</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">m12</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">m21</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">gamma1</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">gamma2</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">h1</span>=<span class="sig-default">0.5</span>,
        <span class="sig-arg">h2</span>=<span class="sig-default">0.5</span>,
        <span class="sig-arg">theta0</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">initial_t</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">frozen1</span>=<span class="sig-default">False</span>,
        <span class="sig-arg">frozen2</span>=<span class="sig-default">False</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="dadi.Integration-pysrc.html#two_pops">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">

Integrate a 2-dimensional phi foward.

phi: Initial 2-dimensional phi
xx: 1-dimensional grid upon (0,1) overwhich phi is defined. It is assumed
    that this grid is used in all dimensions.

nu's, gamma's, m's, and theta0 may be functions of time.
nu1,nu2: Population sizes
gamma1,gamma2: Selection coefficients on *all* segregating alleles
h1,h2: Dominance coefficients. h = 0.5 corresponds to genic selection.
m12,m21: Migration rates. Note that m12 is the rate *into 1 from 2*.
theta0: Propotional to ancestral size. Typically constant.

T: Time at which to halt integration
initial_t: Time at which to start integration. (Note that this only matters
           if one of the demographic parameters is a function of time.)

Note: Generalizing to different grids in different phi directions is
      straightforward. The tricky part will be later doing the extrapolation
      correctly.

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="three_pops"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">three_pops</span>(<span class="sig-arg">phi</span>,
        <span class="sig-arg">xx</span>,
        <span class="sig-arg">T</span>,
        <span class="sig-arg">nu1</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">nu2</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">nu3</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">m12</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">m13</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">m21</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">m23</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">m31</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">m32</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">gamma1</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">gamma2</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">gamma3</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">h1</span>=<span class="sig-default">0.5</span>,
        <span class="sig-arg">h2</span>=<span class="sig-default">0.5</span>,
        <span class="sig-arg">h3</span>=<span class="sig-default">0.5</span>,
        <span class="sig-arg">theta0</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">initial_t</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">frozen1</span>=<span class="sig-default">False</span>,
        <span class="sig-arg">frozen2</span>=<span class="sig-default">False</span>,
        <span class="sig-arg">frozen3</span>=<span class="sig-default">False</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="dadi.Integration-pysrc.html#three_pops">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">

Integrate a 3-dimensional phi foward.

phi: Initial 3-dimensional phi
xx: 1-dimensional grid upon (0,1) overwhich phi is defined. It is assumed
    that this grid is used in all dimensions.

nu's, gamma's, m's, and theta0 may be functions of time.
nu1,nu2,nu3: Population sizes
gamma1,gamma2,gamma3: Selection coefficients on *all* segregating alleles
h1,h2,h3: Dominance coefficients. h = 0.5 corresponds to genic selection.
m12,m13,m21,m23,m31,m32: Migration rates. Note that m12 is the rate 
                         *into 1 from 2*.
theta0: Propotional to ancestral size. Typically constant.

T: Time at which to halt integration
initial_t: Time at which to start integration. (Note that this only matters
           if one of the demographic parameters is a function of time.)

Note: Generalizing to different grids in different phi directions is
      straightforward. The tricky part will be later doing the extrapolation
      correctly.

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="_compute_delj"></a>
<div class="private">
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_compute_delj</span>(<span class="sig-arg">dx</span>,
        <span class="sig-arg">MInt</span>,
        <span class="sig-arg">VInt</span>,
        <span class="sig-arg">axis</span>=<span class="sig-default">0</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="dadi.Integration-pysrc.html#_compute_delj">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">

Chang an Cooper's \delta_j term. Typically we set this to 0.5.

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="_one_pop_const_params"></a>
<div class="private">
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_one_pop_const_params</span>(<span class="sig-arg">phi</span>,
        <span class="sig-arg">xx</span>,
        <span class="sig-arg">T</span>,
        <span class="sig-arg">nu</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">gamma</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">h</span>=<span class="sig-default">0.5</span>,
        <span class="sig-arg">theta0</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">initial_t</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">beta</span>=<span class="sig-default">1</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="dadi.Integration-pysrc.html#_one_pop_const_params">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">

Integrate one population with constant parameters.

In this case, we can precompute our a,b,c matrices for the linear system
we need to evolve. This we can efficiently do in Python, rather than 
relying on C. The nice thing is that the Python is much faster to debug.

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="one_pop_X"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">one_pop_X</span>(<span class="sig-arg">phi</span>,
        <span class="sig-arg">xx</span>,
        <span class="sig-arg">T</span>,
        <span class="sig-arg">nu</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">gamma</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">h</span>=<span class="sig-default">0.5</span>,
        <span class="sig-arg">beta</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">alpha</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">theta0</span>=<span class="sig-default">1.0</span>,
        <span class="sig-arg">initial_t</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">frozen</span>=<span class="sig-default">False</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="dadi.Integration-pysrc.html#one_pop_X">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">

Integrate a 1-dimensional phi foward.

phi: Initial 1-dimensional phi
xx: Grid upon (0,1) overwhich phi is defined.

nu, gamma, and theta0 may be functions of time.
nu: Population size
gamma: Scaled selection coefficient on *all* segregating alleles
h: Dominance coefficient. h = 0.5 corresponds to genic selection. 
   Heterozygous females have fitness 1+2sh and homozygous females have
   fitness 1+2s. Male carriers have fitness 1+2s.
theta0: Propotional to ancestral size. Typically constant.
beta: Breeding ratio, beta=Nf/Nm.
alpha: Male to female mutation rate ratio, beta = mu_m / mu_f.

T: Time at which to halt integration
initial_t: Time at which to start integration. (Note that this only matters
           if one of the demographic parameters is a function of time.)

frozen: If True, population is 'frozen' so that it does not change.
        In the one_pop case, this is equivalent to not running the
        integration at all.

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="_one_pop_const_params_X"></a>
<div class="private">
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_one_pop_const_params_X</span>(<span class="sig-arg">phi</span>,
        <span class="sig-arg">xx</span>,
        <span class="sig-arg">T</span>,
        <span class="sig-arg">nu</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">gamma</span>=<span class="sig-default">0</span>,
        <span class="sig-arg">h</span>=<span class="sig-default">0.5</span>,
        <span class="sig-arg">beta</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">alpha</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">theta0</span>=<span class="sig-default">1</span>,
        <span class="sig-arg">initial_t</span>=<span class="sig-default">0</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="dadi.Integration-pysrc.html#_one_pop_const_params_X">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">

Integrate one population with constant parameters.

In this case, we can precompute our a,b,c matrices for the linear system
we need to evolve. This we can efficiently do in Python, rather than 
relying on C. The nice thing is that the Python is much faster to debug.

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
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